Let f(x) = 4*(1 - x/2); 1 ≤ x ≤ 2.   Find E(x). Find exact value (use fractions).

Q: Find f(x) if f°(x)=cos x with f(0) =1, f'(0) = 2 , and f'(-)=3.

A: Keep on integrating we are end up with an answer. For those constants we need these initial…

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A: Given f(x) = 3x3 + cos(3πx) + 2x,  x≥1   ⇒ f'(x) = 9x2 - 3πsin(3πx) + 2

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A: Given; ex=3-2x,(0,1)

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Q: If f is continuous and ∫31 f (x) dx = 8 , show that f takes on the value 4 at least once on the…

A: Given that f is continuous and ∫31 f (x) dx = 8. We have to prove that, f takes on the value 4 at…

Q: [2-x², x20 Given f(x) = , find the value c so that f(x) will be continuous at all values. x<0 x +C

A: Given that: f(x)=2-x2,    x≥0x+c,      x&lt;0   NOTE: As per our answering guidelines, we can only…

Q: Given the function h (x) = : x+1 Over what interval(s) is h (x) decreasing?

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Q: (a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

A: Consider the given piecewise function

Q: Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0…

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Q: on f(x, y) = 3x + 9y subject to th %3D

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Q: c) lim,→1+ f(x) where f(x) = { V1- x, x 1 | x +1,

A: Given query is to find indicated limits.

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Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and g(2x)dx = 3. %3D 2 Find æg(3x²)dx.

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Q: If f(x) is an even, continuous function for which = 4 and dx = 4, then f (x) dx 3 2

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Q: Find the absolution extrema of f(x) = (In x)2 on [1, e].

A: We have to determine absolute extrema of girls question

Q: 2 If f is continuous and f(x) dx = 14, find | xf(x?) dx.

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Q: (B) Verify the Mean Value Theorem for f(x) = ln(4x + 1) on | 0,

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Q: 1. Suppose that f f(x) dx = In x + Vx+1+C. Can f be a rational function? Explain.

A: To explain f is a rational function or not.

Q: if x3 is continuous at x = 3

A: Given query is to find the value of c so that function is continuous at x = 3.

Q: Find f'(x) for f(x) = 3 arctan(4x² – 3) %3D

A: we use the formula f'(x) of arcton x=1/1+x^2.

Q: 81 xf(x²) dx. 6. If f is continuous and f(x) dx = 4, find

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Q: Find the antiderivative F of the function f(x)= x^2 + 2x + 2 such that F(-1) = -1.  F(x) =

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Q: At what interval is y=3x5-5x3 decreasing O x>1 O -1<x<0 O -1<x< OU 0<x<I O -1<1<l

A: We have to find interval where it is decreasing

Q: 8. If f is continuous and f(x) dx = 12, find f(2x) dx. 0.

A: Given f is continuous and ∫08f(x)dx=12

Q: If f is continuousand ∫31f(x) dx=8, show that f takes on the value 4 at least once on the interval…

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Q: Differentiate f(x) = f'(x) = 2 ax with respect to x. Assume that a and k are positive constants. k+x

A: To differentiate fx=ax2k+x with respect to x. Assume that a and k are positive constants.

Q: Find f'( – 2) for f(x) = ln( (x* + 3)´) as an exact fraction or rounded to at least 2 decimal…

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Q: Let f (x) be equal to -x + 1 for x < 0, equal to 1 for 0 < x < 1, equal to –x + 2 for 1 < x.…

A: Definition of the function in the different intervals helps to integrate the given function.…

Q: If f is continuous and f(x)dx=4, xf(x2)dx=

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Q: For f(x) = Vx ln x, find a). domain and f', b). the intervals on which f is increasing or…

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Q: Suppose f'(x) = c for all x, where c is a constant. Show that, for some constant d, f(x) = cx + d.

A: suppose f'(x) =c for all x, where c is constant .Show that for some constant d, f(x)=cx+d

Q: Determine the domain of the function f(x) = In(ln r) + x

A: f(x) = ln(ln x) + x f(x) is not defined if ln x &lt;= 0 [as then ln(ln x) is not defined] ln x &lt;=…

Q: Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and…

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Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 When is the function concave up and concave down in…

A: For concavity we need second derivative.

Q: find f'(x) for f(x) = 2xtan-1 x - ln(1+x2)

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Q: If b > 3 and average value of f(x) = 6x – x² on the interval [0,b] is 6, then what is b equal to?

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Q: f is continuous and f(x) dx = 8, find xfc

A: we have to find

Q: Suppose that a continuous function g satisfies: | g(x)dx = 12 and g(2x)dx = 27. Find æg(3x²)dx.

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Q: Determine the value of the arbitrary constant of the antriderivative of F(x) = x-In(x) given the…

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Q: Find all the x-intercepts of f(x)=cos(x) on the interval [0,2π)

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Q: x3 B- If f(x) = ;, Find A? is continuous at x = %3D (Ax² x 2 1/N IN V

A: Given: f(x)=x3x&lt;12Ax2x≥12 Since f(x) is continuous at x=12. limx→12-f(x)=limx→12+f(x)

Q: If f(x) = x2+1 for x > or equal to 0, then is arcf(x) has a tangent at x=1

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Q: For every continuous f:[0,+0) →R _function , if a>0 2fx'f(x*)dx =[ xf(x)dx Demonstrate that this…

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Q: Find f(x) if f(3) = 0 and the tangent line at (x, f(x)) has slope x2 + 5 In (14) f(x) =| 히n 글미(구+ 5)…

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Q: a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

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Q: Find a value of k making h(x) continuous on (0, 5). 0 < x < 2 2 < x < 5 h(x) = x +1,

A: A function is continuous if limx→a+ h(x)  = limx→a- h(x) = h(a) Now in the given question, function…

Q: Use the e-d definition to prove that f(x) = x³ + 3 is continuous at xo = 3.

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Q: Suppose that f (x) is a continuous function. 3 If | f(x) dx=5, then what is the value of z - f(x)]…

A: Given, ∫13f(x) dx =5Now,∫13[x -f(x)] dx= ∫13x dx -∫13f(x) dx =x2213 -5…

Q: If f(x)=e^cosh(4x) then f'(x)=

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